Publication detail

The de Groot dual for general collections of sets

KOVÁR, M.

Original Title

The de Groot dual for general collections of sets

English Title

The de Groot dual for general collections of sets

Type

conference paper

Language

en

Original Abstract

A topology is de Groot dual of another topology, if it has a closed base consisting of all its compact saturated sets. Until 2001 it was an unsolved problem of J. Lawson and M. Mislove whether the sequence of iterated dualizations of a topological space is finite. In this paper we generalize the author's original construction to an arbitrary family instead of a topology. Among other results we prove that for any family $\C\subseteq 2^X$ it holds $\C^{dd}=\C^{dddd}$. We also show similar identities for some other similar and topology-related structures.

English abstract

A topology is de Groot dual of another topology, if it has a closed base consisting of all its compact saturated sets. Until 2001 it was an unsolved problem of J. Lawson and M. Mislove whether the sequence of iterated dualizations of a topological space is finite. In this paper we generalize the author's original construction to an arbitrary family instead of a topology. Among other results we prove that for any family $\C\subseteq 2^X$ it holds $\C^{dd}=\C^{dddd}$. We also show similar identities for some other similar and topology-related structures.

RIV year

2004

Released

14.10.2004

Publisher

IBFI Schloss Dagstuhl

Location

Schloss Dagstuhl, Deutschland

Pages from

1

Pages to

8

Pages count

8

URL

ftp://ftp.dagstuhl.de/pub/Proceedings/04/04351/04351.KovarMartin5.Paper!.pdf

Documents

BibTex


@inproceedings{BUT11708,
  author="Martin {Kovár}",
  title="The de Groot dual for general collections of sets",
  annote="A topology is de Groot dual of another topology, if it has a closed base consisting of
all its compact saturated sets. Until 2001 it was an unsolved problem of J. Lawson and M. Mislove
whether the sequence of iterated dualizations of a topological space is finite. In this paper we
generalize the author's original construction to an arbitrary family instead of a topology. Among
other results we prove that for any family $\C\subseteq 2^X$ it holds $\C^{dd}=\C^{dddd}$.  We also
show similar identities for some other similar and topology-related structures.",
  address="IBFI  Schloss Dagstuhl",
  booktitle="Proceedings of the Dagstuhl Seminar 04351 - Spatial Representation: Discrete vs. Continuous Computational Models",
  chapter="11708",
  institution="IBFI  Schloss Dagstuhl",
  number="04351",
  year="2004",
  month="october",
  pages="1",
  publisher="IBFI  Schloss Dagstuhl",
  type="conference paper"
}